Baumslag [Bm1] and Remeslennikov [R1] independently showed that the abstract group with finite presentation

〈a, x, y[mid ]ax =aay, [x, y] =1=[a, ay]〉.

is metabelian; the derived subgroup is free abelian of countably infinite rank. Both generalized this example to show that every finitely generated metabelian group embeds in a finitely presented metabelian group. Thomson [T] generalized this result still further to show that every finitely generated group of upper triangular matrices over an abstract ring A lies inside a finitely presented group of upper triangular matrices over some extension ring of A. For a valuable survey of these results, see [St].

Baumslag proved analogous theorems for Lie algebras in [Bm2]. In this paper we shall prove some analogous results for pro-p groups.